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Abstract: The similarity transformation between the ( )-dimensional nonlinear Schrödinger equation with different distributed transverse diffraction and the standard nonlinear Schrödinger equation is found, and a spatiotemporal breather solution is given based on this transformation. The control for the evolutional behaviors of a spatiotemporal breather is discussed. Our results manifest that the relation between the maximum accumulated time and the accumulated time, , with the maximum amplitude, is the basis to realize the control and manipulation of propagation behaviors of breathers, such as fast and slow excitations, sustainment and restraint. These results are potentially useful for future experiments in the optical communications and Bose–Einstein condensations. [Copyright &y& Elsevier]

The dynamic unbalance of the rotor on a satellite produces unexpected disturbing torque and affects satellite attitude, so the amount of dynamic unbalance must be controlled in the high quality movement control of the satellite. The flexible multi-body dynamics model is built, meanwhile, residual disturbing torque of the rotor is analyzed by using the dynamic balance test, the control method and process for dynamic balance of large-scale rotary payload are proposed. Finally, practice engineering application and on orbit telemetry demonstrate that the control method and process of dynamic balancing are feasible and effective. [ABSTRACT FROM AUTHOR]

Abstract: Three algorithms based on the bifurcation method are applied to solving the D 4(3) symmetric positive solutions to the boundary value problem of Henon equation. Taking r in Henon equation as a bifurcation parameter, the symmetry-breaking bifurcation points are found via the extended systems on the branch of the D 4(3) symmetric positive solutions. Finally, other symmetric positive solutions are computed by the branch switching method based on the Liapunov–Schmidt reduction. [Copyright &y& Elsevier]

Abstract: Starting from a special variable transformation and an extended mapping approach, the (1+1)-dimensional Korteweg–de Vries (KdV) type model related to nonlinear Schrödinger system is solved, and families of variable separation solutions with arbitrary functions are derived. Then based on the derived exact solution, we reveal some periodic loop solitons and chaotic solitons for the (1+1)-dimensional KdV type model. [Copyright &y& Elsevier]

Abstract: Starting from a special Painlevé–Bäcklund transformation, the nonlinear generalized Broer–Kaup(GBK) system in (2+1)-dimensions is reduced to a linear system. Then by means of the linear superposition theorem, a general variable separation excitation to the generalized Broer–Kaup system is obtained. Finally, based on the derived solution, a new type of localized structure, i.e., semifolded localized coherent structure is constructed and some evolution properties of the novel semifolded localized structure are briefly discussed. [Copyright &y& Elsevier]

A method of on-orbit modal calculation suitable for the engineering application is presented in this article. Firstly, the finite element model should be corrected through the ground test, and the constraint modal results of flexible appendages will be extracted. Combining with the dynamics equation of entire satellite, the constraint modal will be translated into unconstraint modal by using the eigenvalue method. The example shows that the method in this article can calculate the on-orbit modal frequency accurately. In engineering, the error of on-orbit frequency will be under 15%. [ABSTRACT FROM AUTHOR]